Name:
Scalars and Vectors
Time: 45 minutes
LEVEL
SUBJECT
EXAM BOARD
IGCSE
Physics
Cambridge Assesment International Examination
INSTRUCTIONS
•
•
•
•
Answer all questions.
You may use a calculator.
You should show all your working and use appropriate units.
Take the weight of 1.0 kg to be 9.8 N (acceleration of free fall = 9.8 m/s2).
INFORMATION
• The total mark for this paper is 69
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Fig. 1.1 shows a straight section of a river where the water is flowing from right to left at a speed of
0.54 m / s.
river
current
0.54 m / s
P
swimmer
Fig. 1.1 (not to scale)
A swimmer starts at point P and swims at a constant speed of 0.72 m / s relative to the water and at
right angles to the current.
(a) (i)
Determine, relative to the river bank, both the magnitude and direction of the swimmer’s
velocity.
magnitude of velocity = ...............................................................
direction of velocity ...............................................................
[4]
(ii)
After 1.5 minutes, the swimmer reaches point Q.
Calculate the distance between P and Q.
distance = ......................................................... [3]
1
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(b) When the swimmer is crossing the river, his actions produce a constant forward force on his
body.
Explain why he moves at a constant speed.
...................................................................................................................................................
...................................................................................................................................................
...................................................................................................................................................
............................................................................................................................................. [2]
[Total: 9]
2
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(a) A boat crosses a river. The boat points at right angles to the river bank and it travels at a
speed of 3.5 m / s relative to the water.
A river current acts at right angles to the direction the boat points. The river current has a
speed of 2.5 m / s.
By drawing a scale diagram or by calculation, determine the speed and direction of the boat
relative to the river bank.
speed = ...............................................................
direction relative to the river bank = ...............................................................
[4]
(b) Speed is a scalar quantity and velocity is a vector quantity.
State the names of one other scalar quantity and one other vector quantity.
scalar quantity ..........................................................................................................................
vector quantity ..........................................................................................................................
[2]
[Total: 6]
3
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(a) Fig. 3.1 shows water in a river moving parallel to the river bank at 4.0 m / s and a canoe
travelling in the river.
river bank
38°
canoe travels at 2.5 m / s
relative to the water
water moving at 4.0 m / s
river bank
Fig. 3.1
The canoe travels at 2.5 m / s relative to the water and heads at an angle of 38° to the river
bank.
Draw a scale diagram to determine the canoe’s resultant velocity and state the scale you
used.
scale ...............................................................
magnitude of resultant velocity ...............................................................
direction of resultant velocity (angle from the river bank) ...............................................................
[4]
4
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(b) The mass of the canoeist is 65 kg.
Calculate her kinetic energy when travelling on still water at 2.5 m / s.
energy = ......................................................... [2]
[Total: 6]
5
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(a) Fig. 3.1 shows a boat stored in a shed. The boat is suspended from the ceiling of the shed by
two ropes.
ceiling
60°
T
60°
ropes
T
boat
Fig. 3.1
The tension T in each of the ropes is 75 N.
(i)
Draw a vector diagram to determine the resultant of the forces exerted by the two ropes
on the boat. State the scale you used.
scale = ...............................................................
magnitude of resultant force = ...............................................................
direction of resultant force = ......................................................... [4]
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(ii)
Determine the mass of the boat.
mass = ......................................................... [1]
(b) Force is a vector.
Draw a circle around two other quantities in the list which are vectors.
acceleration
momentum
density
energy
power
mass
refractive index
[2]
[Total: 7]
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A woman starts to push a trolley across the floor. Fig. 5.1 shows the horizontal forces acting on the
trolley.
trolley
120 N
90 N
Fig. 5.1
(a) Determine the resultant horizontal force on the trolley.
resultant force = ............................................................ N
direction of resultant force = ...............................................................
[3]
7
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6 (i) Speed is a scalar quantity and velocity is a vector quantity. State the difference between
a scalar quantity and a vector quantity.
...........................................................................................................................................
..................................................................................................................................... [2]
(ii)
Write down one other scalar quantity and one other vector quantity.
scalar quantity ...................................................................................................................
vector quantity ...................................................................................................................
[2]
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(c) Fig. 2.2 shows two forces acting on an object.
60°
30 N
20 N
Fig. 2.2 (not to scale)
Draw a scale diagram to determine the resultant force acting on the object. State the scale
you use.
scale ..............................................................
magnitude of resultant force = ...........................................................
direction of resultant relative to the direction of the 20 N force = ...........................................................
[4]
[Total: 8]
9
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Some physical quantities are scalars and other physical quantities are vectors.
(a) State how a vector quantity differs from a scalar quantity.
...................................................................................................................................................
............................................................................................................................................. [1]
(b) Circle the vector quantities in the list.
acceleration
energy
mass
momentum
temperature
time
speed
velocity
[2]
(c) A microphone in a recording studio has a mass of 0.55 kg and a weight W.
(i)
Calculate W.
W = .......................................................... [1]
(ii)
The microphone is suspended from the ceiling by a cord attached to a small ring. Fig. 1.1
shows the microphone pulled to one side and kept stationary by a horizontal thread.
ceiling
cord
ring
horizontal thread
microphone
Fig. 1.1 (not to scale)
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The tension T in the horizontal thread is 8.1 N.
Determine graphically the magnitude and the direction, relative to the vertical, of the
resultant of W and T. Use a scale of 1.0 cm to 1.0 N or greater.
magnitude of resultant = ................................................................
direction of resultant = ................................... relative to vertical
[3]
(iii)
State and explain how the magnitude and direction of the resultant in (c)(ii) compares
with the force on the ring due to the tension in the cord.
...........................................................................................................................................
...........................................................................................................................................
..................................................................................................................................... [2]
[Total: 9]
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Fig. 1.1 shows an ice-hockey player moving on ice. He is preparing to hit the solid disc called a
puck.
ice-hockey player
ice
hockey stick
disc
Fig. 1.1
The disc of mass 0.16 kg is moving horizontally across the surface of the ice at a speed of 15 m / s.
(a) Calculate the magnitude of the momentum of the disc.
magnitude of momentum = ......................................................... [2]
(b) The hockey player strikes the disc with his hockey stick and the momentum of the disc
changes. The disc gains momentum of 3.0 kg m / s at 45° to the original direction of travel of
the disc, as shown in Fig. 1.2.
direction of
momentum gained
disc
45°
original direction of travel
Fig. 1.2 (view from above)
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(i)
State the magnitude of the impulse exerted on the disc and the direction, in degrees, of
the impulse relative to the original direction of travel.
magnitude of impulse = ...............................................................
direction of impulse:
(ii)
............................ ° to original direction
[1]
Determine the magnitude of the new momentum of the disc and its new direction relative
to the original direction of travel by drawing a scale diagram.
magnitude of new momentum = ...............................................................
direction of new momentum:
........................... ° to original direction
[4]
[Total: 7]
13
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(a) An object is moving in a straight line at constant speed.
State three ways in which a force may change the motion of the object.
1 ...............................................................................................................................................
2 ...............................................................................................................................................
3 ...............................................................................................................................................
[2]
(b) Fig. 3.1 shows an object suspended from two ropes. The weight of the object is 360 N. The
magnitude of the tension in each rope is T.
T
T
45°
45°
object
360 N
Fig. 3.1
In the space below, determine the tension T by drawing a vector diagram of the forces acting
on the object.
State the scale you have used.
scale ...............................................................
T = ...............................................................
[5]
[Total: 7]
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10 (a) (i)
Speed is a scalar quantity and velocity is a vector quantity.
State how a scalar quantity differs from a vector quantity.
...........................................................................................................................................
.......................................................................................................................................[1]
(ii)
Underline the two scalar quantities in the list below.
energy
force
impulse
momentum
temperature
[1]
(b) A boat is moving at constant speed.
On Fig. 1.1, sketch a distance-time graph for the boat.
distance
time
Fig. 1.1
[1]
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(c) The boat in (b) is moving due west at a speed of 6.5 m / s relative to the water. The water is
moving due south at 3.5 m / s.
In the space below, draw a scale diagram to determine the size and direction of the resultant
of these two velocities. State the scale used.
scale ...............................................................
size of resultant velocity = ...............................................................
direction of resultant ...............................................................
[4]
[Total: 7]
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